You generally use for to specify an amount of time, for example
I was in hospital for three days
You use in when you describe what happened or will happen during a period of time, for example
I will be going to Cairo in July
Note that both prepositions have several other possible usages: I have just highlighted those that apply to your question.
In your example, you are talking about what will happen, so in is the correct preposition to use.
This news augurs happiness in the days to come
Note that we do not normally use the before abstract nouns like happiness. See the abstract nouns section of this link.